The infimum of the energy of unit vector fields on odd-dimensional spheres
type: Item
instance of: scholarly article
title: The infimum of the energy of unit vector fields on odd-dimensional spheres
zbMATH Open document ID: 1031.53090
DOI: 10.1023/A:1022404728764
author: Vincent Borrelli
author: O. Gil-Medrano
author: Fabiano G. B. Brito
published in: Annals of Global Analysis and Geometry
publication date: 2003-06-09T00:00:00Z
review text: Let \(M\) be an oriented, closed, \(n\)-dimensional Riemannian manifold and \(T^1M\) be the unit tangent bundle of \(M\) considered as a closed Riemannian manifold with the Sasaki metric. The energy of a unit smooth vector field \(v\) on \(M\) is \(E(v)= {1\over 2}\int_M(n+\|\nabla\|^2)dM\), where \(dM\) is the volume form on \(M\). The authors construct a one-parameter family of unit smooth vector fields globally defined on the sphere \(\mathbb{S}^{2k +1}\) for \(k\geq 2\), with energy converging to the energy of the unit radial vector field defined on the complement of two antipodal points. The infimum of the energy of these vector fields is \(({2k+1\over 2}+ {k\over 2k-1}) \text{vol} (\mathbb{S}^{2k+1})\).
Mathematics Subject Classification ID: 53C43
Mathematics Subject Classification ID: 58E15
zbMATH DE Number: 1925034
zbMATH Keywords: energy of a vector field
zbMATH Keywords: radial fields on spheres
zbMATH Keywords: minimizing sequence
zbMATH Keywords: Sasaki metric
reviewed by: Vasile Oproiu
MaRDI profile type: Publication
full work available at URL: a:1022404728764
OpenAlex ID: W2291391405
description: scientific article; zbMATH DE number 1925034